CN106844985B - A kind of fast solution method and system of high-freedom degree Robotic inverse kinematics - Google Patents
A kind of fast solution method and system of high-freedom degree Robotic inverse kinematics Download PDFInfo
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Abstract
The present invention proposes the fast solution method and system of a kind of high-freedom degree Robotic inverse kinematics, the method comprising the steps of 1, and joint variable θ is brought into Robot kinematics equations, obtains Jacobian matrix J, the Jacobian matrix J is subjected to transposition, obtains Jacobi transposed matrix JT；Step 2, it generates one group and speculates value, calculate corresponding joint variable updated value each to speculate value, each joint variable updated value is brought into robot forward kinematics equation, corresponding pose P is obtainedk, it is each pose PkCalculate its pose deviation delta e with object pose PkAnd pose deviation delta ekMould errork；Step 3, in mould errorkSet in choose minimum value errorminAnd its corresponding pose deviation delta eminWith joint variable updated value Δ θmin, and updating pose deviation is Δ e=Δ emin, update joint variable θ=θ+Δ θmin；Step 4, judge errorminWhether error is metminOtherwise < Threshold, returns to the step 1, continues to execute if it is, exporting joint variable θ and terminating.
Description
Technical field
The present invention relates to technical field of robot control, in particular to a kind of high-freedom degree Robotic inverse kinematics it is quick
Method for solving and system.
Background technique
Robot technology can be applied not only to industrial production, and can serve people's life, is one and answers very much
With the technology of prospect.Robot is usually to be made of many joints, by controlling each joint variable, reaches the function of pose variation
Can, such as move, walk and grab etc..In robotics, each joint respectively provides one degree of freedom.Generally, machine
The freedom degree of device people is more (joint is more), and robot function is more powerful, and movement is more flexible.Robot kinematics are machines
The basis of people's motion control includes positive kinematics and inverse kinematics.Positive kinematics give each joint variable θ, solve machine
The pose P of people；Inverse kinematics, i.e., the pose P of given robot, solves the joint variable θ in each joint of robot, such as Fig. 1 institute
Show.Positive kinematics can be by solving kinematic equation, and solution procedure is relatively easy, on the contrary, inverse kinematics are complicated, consumption
When, it is even worse for high-freedom degree robot situation.Currently, solution of Inverse Kinematics mainly uses: analytic method, numerical method and
Machine learning method.
Analytic method can be easy to solve Inverse Kinematics Problem by constructing inverse kinematics equation.But for any
For robot, building inverse kinematics equation is extremely complex, and there is no inverse kinematics equations for many situations.Therefore,
Analytic method can only be applied in specific robot or mechanical arm, and the freedom degree of robot or mechanical arm can only be seldom.
Numerical method generally requires and finds the approximate solution for meeting certain required precision by successive ignition.Wherein, it transports
With it is most be the method based on Jacobi, compare other numerical methods, this method is more accurate, stablizes.Based on Jacobi
Method for solving includes two classes again: Jacobi pseudoinverse technique and Jacobi transposition method.The convergence of Jacobi pseudoinverse technique is fast, but needs to carry out
Singular value decomposition operation, complicated and time consumption are difficult parallel；On the contrary, Jacobi transposition method needs iteration many times, still, each iteration
Operation is simple, quickly.
Machine learning method carries out approximation to inverse kinematics equation using the method for machine learning, thus in finite time
Obtain approximate solution.But the problem of this method maximum is that approximate solution and the deviation accurately solved are larger, is obtained much larger than numerical method
Approximate solution.Meanwhile this method needs mass data to be trained.
Currently, most common inverse kinematics method is the method for solving based on Jacobi, but to high-freedom degree machine
For device people, the existing method based on Jacobi is very time-consuming, is not able to satisfy the requirement of real-time of robot control, for this purpose,
The present invention proposes a kind of rapid solving high-freedom degree Robot Inverse Kinematics Problem executed suitable for parallel architecture
Method.
Original Jacobi transposition method firstly generates a parameter value α, then more according to the parameter in each iterative process
New joint variable θ, is shown in attached drawing 2, inventor has found that the selection of the reference value alpha seriously affects solving speed, proposes thus
A kind of choosing method speculated parallel.This method in each iteration, generates multiple parameter values (speculating value) α 1, α 2 ... α m,
The available multiple joint variable updated value of the parameter value different according to these, then therefrom select the parameter closest to target solution
Value and joint variable updated value, calculating due to multiple parameter values and subsequent joint variable updated value calculate between not according to
Rely, can be performed simultaneously by parallel organization, to accelerate solving speed.
Summary of the invention
In view of the deficiencies of the prior art, the present invention proposes a kind of fast solution method of high-freedom degree Robotic inverse kinematics
And system.
The present invention proposes a kind of fast solution method of high-freedom degree Robotic inverse kinematics, comprising:
Step 1, joint variable θ is brought into Robot kinematics equations, Jacobian matrix J is obtained, by the Jacobi
Matrix J carries out transposition, obtains Jacobi transposed matrix JT；
Step 2, it generates one group and speculates value, corresponding joint variable updated value is calculated each to speculate value, by each joint
Variable update value is brought into robot forward kinematics equation, and corresponding pose P is obtainedk, it is each pose PkCalculate itself and target position
The pose deviation delta e of appearance PkAnd pose deviation delta ekMould errork；
Step 3, in mould errorkSet in choose minimum value errorminAnd its corresponding pose deviation delta eminWith pass
Save variable update value Δ θmin, and updating pose deviation is Δ e=Δ emin, update joint variable θ=θ+Δ θmin；
Step 4, judge errorminWhether error is metmin< Threshold, wherein Threshold is preset
errorminOtherwise threshold value, returns to the step 1, continues to execute if it is, exporting joint variable θ and terminating.
It further include one group of initial value θ of random generation before the step 1init, and enable θ=θinit；
Joint variable θ is brought into robot forward kinematics equation, corresponding pose P is obtainedinit；
Calculate pose PinitWith the pose deviation delta e=P-P of object pose PinitAnd the mould error of pose deviation delta e；
Judge whether mould error meets error < Threshold, if it is, export joint variable θ and terminate, otherwise,
Execute the step 1.
Value is each speculated in the step 2 and is greater than 0, less than 1.
It is the formula that each congenial value calculates corresponding joint variable updated value in the step 2 are as follows:
Δθk=αk JTΔe
Wherein Δ θkFor joint variable updated value, αkTo speculate value, JTFor Jacobi transposed matrix, Δ e is pose deviation.
Described m computational threads of unlatching, per thread generates one and speculates value, wherein k-th of thread generates and speculate value αk,
Calculation formula are as follows:
Wherein αkTo speculate value, Δ e is pose deviation, JTFor Jacobi transposed matrix, Jacobian matrix J.
The present invention also proposes a kind of rapid solving system of high-freedom degree Robotic inverse kinematics, comprising:
Jacobi transposed matrix module is obtained, for bringing joint variable θ in Robot kinematics equations into, obtains refined gram
Than matrix J, the Jacobian matrix J is subjected to transposition, obtains Jacobi transposed matrix JT；
Pose tolerance module is obtained, speculates to be worth for generating one group, speculates the corresponding joint variable of value calculating more to be each
New value, each joint variable updated value is brought into robot forward kinematics equation, corresponding pose P is obtainedk, it is each pose
PkCalculate its pose deviation delta e with object pose PkAnd pose deviation delta ekMould errork；
Joint variable module is updated, in mould errorkSet in choose minimum value errorminAnd its corresponding position
Appearance deviation delta eminWith joint variable updated value Δ θmin, and updating pose deviation is Δ e=Δ emin, update joint variable θ=θ+
Δθmin；
Judgment module, for judging errorminWhether error is metmin< Threshold, wherein Threshold is default
ErrorminOtherwise threshold value, returns to the acquisition Jacobi transposed matrix mould if it is, exporting joint variable θ and terminating
Block continues to execute.
It further include one group of initial value θ of random generation before the acquisition Jacobi transposed matrix moduleinit, and enable θ=
θinit；
Joint variable θ is brought into robot forward kinematics equation, corresponding pose P is obtainedinit；
Calculate pose PinitWith the pose deviation delta e=P-P of object pose PinitAnd the mould error of pose deviation delta e；
Judge whether mould error meets error < Threshold, if it is, export joint variable θ and terminate, otherwise,
Execute the step 1.
Value is each speculated in the acquisition pose tolerance module and is greater than 0, less than 1.
It is the formula that each congenial value calculates corresponding joint variable updated value in the acquisition pose tolerance module are as follows:
Δθk=αk JTΔe
Wherein Δ θkFor joint variable updated value, αkTo speculate value, JTFor Jacobi transposed matrix, Δ e is pose deviation.
Described m computational threads of unlatching, per thread generates one and speculates value, wherein k-th of thread generates and speculate value αk,
Calculation formula are as follows:
Wherein αkTo speculate value, Δ e is pose deviation, JTFor Jacobi transposed matrix, Jacobian matrix J.By above scheme
It is found that the present invention has the advantages that
The easy parallelization of the present invention: fast solution method proposed by the present invention improves Jacobi transposition method, makes it suitable for
It is executed in parallel architecture, such as multi-core processor, image processor etc.；
High real-time: by executing the algorithm in parallel architecture, can effectively accelerate inverse kinematics, thus
This method is allowed to obtain satisfactory result within a very short time.
Detailed description of the invention
Fig. 1 is inverse kinematics schematic diagram；
Fig. 2 is original Jacobi transposition method flow chart；
Fig. 3 is the fast solution method flow chart of inverse kinematics；
Fig. 4 is high-freedom degree robot schematic diagram.
Specific embodiment
The following are overall flows of the invention, as shown in figure 3, the method for the present invention includes:
Step 1 generates one group of initial value θ at randominit, and enable θ=θinit；
Step 2 brings joint variable θ in robot forward kinematics equation into, finds out corresponding pose Pinit=f (θ)；
Step 3 calculates pose PinitWith the deviation delta e=P-P of object pose PinitAnd the mould error of deviation delta e；
Step 4, judges whether error meets required precision, i.e. error < Threshold, if so, output joint becomes
Amount θ simultaneously terminates, and otherwise, continues to execute step 5.
Step 5 brings joint variable θ in Robot kinematics equations into, finds out Jacobian matrix J；
Jacobian matrix transposition is obtained Jacobi transposed matrix J by step 6T；
Step 7 generates one group and speculates value α1,α2,α3,...αm, and each congenial value is greater than 0, less than 1；
Step 8, for each congenial value αk, calculate corresponding joint variable updated value Δ θk=αkJTΔe；
Step 9, by each joint variable updated value Δ θkIt brings into robot forward kinematics equation, finds out corresponding position
Appearance Pk=f (θ+Δ θk)；
Step 10 is each pose PkCalculate its pose deviation delta e with object pose Pk=P-PkAnd pose deviation delta
ekMould errork；
Step 11, in error1,error2,...errormMiddle selection minimum value errorminAnd its corresponding pose is inclined
Poor Δ eminWith joint variable updated value Δ θmin, and update pose deviation delta e=Δ emin, update joint variable θ=θ+Δ θmin；
Step 12 judges errorminWhether required precision, i.e. error are metmin< Threshold, if so, output
Joint variable θ simultaneously terminates, and otherwise, returns to step 5, continues to execute.
The following are a kind of efficient mechanism congenial parallel of the invention, shown in attached drawing 3:
Step 1 opens m computational threads；
Step 2, per thread generates one and speculates value, wherein k-th of thread generates and speculate value αk, calculation is as follows:
Step 3, the congenial value α that per thread is generated according to itselfk, carry out pose and calculate Pk=f (θ+Δ θk) and pose
Deviation calculates Δ ek=P-Pk；
Step 4 collects all threads and calculates resulting pose deviation delta e1, Δ e2,…Δem, it is the smallest to choose wherein mould
Pose deviation delta eminAnd its corresponding congenial value αmin；
Step 5 updates joint variable θ=θ+αk JTΔ e and pose deviation delta e=Δ emin。
Below in conjunction with attached drawing, the present invention is described in detail.
Application environment of the invention is high-freedom degree robot.There are many joints in the robot, while equipping can
With processor of parallel computation, such as multi-core processor (multi-core CPU), image processor (GPU) or customization FPGA etc..Fig. 4
It shows the robot with 20 joints (freedom degree), while being equipped with an image processor GPU for executing inverse fortune
It is dynamic to learn derivation algorithm.
In Fig. 4, the spatial position P (x of handgrip is giveno,yo,zo), then solve the angle, θ (θ in each joint1,θ2,...
θ20)。
Step 1, processor GPU generate 20 numerical value at random and form one group of initial value θinit, and enable θ=θinit；
Step 2, processor GPU bring joint variable θ in Robot kinematics equations into, find out corresponding pose Pinit
=f (θ)；
Step 3, processor GPU calculate initial pose Pinit(xinit,yinit,zinit) and object pose P (xo,yo,zo)
Deviation delta e=P-Pinit=(xo-xinit,yo-yinit,zo-zinit) and deviation delta e mould error；
Step 4, judges whether error meets required precision, i.e. error < Threshold, if so, processor GPI is defeated
Joint variable θ and terminate out, otherwise, executes step 5.
Step 5 brings joint variable θ in Robot kinematics equations into, finds out Jacobian matrix J；
Jacobian matrix transposition is obtained Jacobi transposed matrix J by step 6T；
Step 7 generates m congenial value α1,α2,α3,...αm, and each congenial value is greater than 0, less than 1；
Step 8, processor GPU are each to speculate value αkA computational threads are distributed, per thread is responsible for calculating corresponding
Joint variable updated value Δ θk=αk JTΔe；
Step 9, by each joint variable updated value Δ θkIt brings into robot forward kinematics equation, finds out corresponding position
Appearance Pk=f (θ+Δ θk)；
Step 10 is each pose PkCalculate its pose deviation delta e with object pose Pk=P-PkAnd pose deviation delta
ekMould errork；
Step 11, in error1,error2,...errormMiddle selection minimum value errorminAnd its corresponding pose is inclined
Poor Δ eminWith joint variable updated value Δ θmin, and update pose deviation delta e=Δ emin, update joint variable θ=θ+Δ θmin；
Step 12 judges errorminWhether required precision, i.e. error are metmin< Threshold, if so, output
Joint variable θ simultaneously terminates, and otherwise, returns to step 5, continues to execute.
The present invention also proposes a kind of rapid solving system of high-freedom degree Robotic inverse kinematics, comprising:
Jacobi transposed matrix module is obtained, for bringing joint variable θ in Robot kinematics equations into, obtains refined gram
Than matrix J, the Jacobian matrix J is subjected to transposition, obtains Jacobi transposed matrix JT；
Pose tolerance module is obtained, speculates to be worth for generating one group, speculates the corresponding joint variable of value calculating more to be each
New value, each joint variable updated value is brought into robot forward kinematics equation, corresponding pose P is obtainedk, it is each pose
PkCalculate its pose deviation delta e with object pose PkAnd pose deviation delta ekMould errork；
Joint variable module is updated, in mould errorkSet in choose minimum value errorminAnd its corresponding position
Appearance deviation delta eminWith joint variable updated value Δ θmin, and updating pose deviation is Δ e=Δ emin, update joint variable θ=θ+
Δθmin；
Judgment module, for judging errorminWhether error is metmin(wherein Threshold is default to < Threshold
ErrorminThreshold value can wait numerical value according to design requirement for 0.1,0.05), if it is, export joint variable θ and terminate,
Otherwise, the acquisition Jacobi transposed matrix module is returned to, is continued to execute.
It further include one group of initial value θ of random generation before the acquisition Jacobi transposed matrix moduleinit, and enable θ=
θinit；
Joint variable θ is brought into robot forward kinematics equation, corresponding pose P is obtainedinit；
Calculate pose PinitWith the pose deviation delta e=P-P of object pose PinitAnd the mould error of pose deviation delta e；
Judge whether mould error meets error < Threshold, if it is, export joint variable θ and terminate, otherwise,
Execute the step 1.
Value is each speculated in the acquisition pose tolerance module and is greater than 0, less than 1.
It is the formula that each congenial value calculates corresponding joint variable updated value in the acquisition pose tolerance module are as follows:
Δθk=αk JTΔe
Wherein Δ θkFor joint variable updated value, αkTo speculate value, JTFor Jacobi transposed matrix, Δ e is pose deviation.
Described m computational threads of unlatching, per thread generates one and speculates value, wherein k-th of thread generates and speculate value αk,
Calculation formula are as follows:
Wherein αkTo speculate value, Δ e is pose deviation, JTFor Jacobi transposed matrix, Jacobian matrix J.
Claims (10)
1. a kind of fast solution method of high-freedom degree Robotic inverse kinematics characterized by comprising
Step 1, joint variable θ is brought into Robot kinematics equations, Jacobian matrix J is obtained, by the Jacobian matrix J
Transposition is carried out, Jacobi transposed matrix J is obtainedT；
Step 2, it generates one group and speculates value, corresponding joint variable updated value is calculated each to speculate value, by each joint variable
Updated value is brought into robot forward kinematics equation, and corresponding pose P is obtainedk, it is each pose PkCalculate itself and object pose P
Pose deviation delta ekAnd pose deviation delta ekMould errork；
Step 3, in mould errorkSet in choose minimum value errorminAnd its corresponding pose deviation delta eminBecome with joint
Measure updated value Δ θmin, and updating pose deviation is Δ e=Δ emin, update joint variable θ=θ+Δ θmin；
Step 4, judge errorminWhether error is metmin< Threshold, wherein Threshold is preset errorminThreshold
Otherwise value, returns to the step 1, continues to execute if it is, exporting joint variable θ and terminating.
2. the fast solution method of high-freedom degree Robotic inverse kinematics as described in claim 1, which is characterized in that the step
It further include one group of initial value θ of random generation before rapid 1init, and enable θ=θinit；
Joint variable θ is brought into robot forward kinematics equation, corresponding pose P is obtainedinit；
Calculate pose PinitWith the pose deviation delta e=P-P of object pose PinitAnd the mould error of pose deviation delta e；
Judge whether mould error meets error < Threshold, if it is, exporting joint variable θ and terminating, otherwise, executes
The step 1.
3. the fast solution method of high-freedom degree Robotic inverse kinematics as described in claim 1, which is characterized in that the step
Value is each speculated in rapid 2 and is greater than 0, less than 1.
4. the fast solution method of high-freedom degree Robotic inverse kinematics as described in claim 1, which is characterized in that the step
It is the formula that each congenial value calculates corresponding joint variable updated value in rapid 2 are as follows:
Δθk=αkJTΔe
Wherein Δ θkFor joint variable updated value, αkTo speculate value, JTFor Jacobi transposed matrix, Δ e is pose deviation.
5. the fast solution method of high-freedom degree Robotic inverse kinematics as described in claim 1, which is characterized in that open m
A computational threads, per thread generates one and speculates value, wherein k-th of thread generates and speculate value αk, calculation formula are as follows:
Wherein αkTo speculate value, Δ e is pose deviation, JTFor Jacobi transposed matrix, J is Jacobian matrix.
6. a kind of rapid solving system of high-freedom degree Robotic inverse kinematics characterized by comprising
Jacobi transposed matrix module is obtained, for bringing joint variable θ in Robot kinematics equations into, obtains Jacobi square
The Jacobian matrix J is carried out transposition, obtains Jacobi transposed matrix J by battle array JT；
Pose tolerance module is obtained, speculates to be worth for generating one group, speculates the corresponding joint variable updated value of value calculating to be each,
Each joint variable updated value is brought into robot forward kinematics equation, corresponding pose P is obtainedk, it is each pose PkIt calculates
The pose deviation delta e of itself and object pose PkAnd pose deviation delta ekMould errork；
Joint variable module is updated, in mould errorkSet in choose minimum value errorminAnd its corresponding pose is inclined
Poor Δ eminWith joint variable updated value Δ θmin, and updating pose deviation is Δ e=Δ emin, update joint variable θ=θ+Δ
θmin；
Judgment module, for judging errorminWhether error is metmin< Threshold, wherein Threshold is preset
errorminOtherwise threshold value, returns to the acquisition Jacobi transposed matrix module if it is, exporting joint variable θ and terminating,
It continues to execute.
7. the rapid solving system of high-freedom degree Robotic inverse kinematics as claimed in claim 6, which is characterized in that described to obtain
It further include one group of initial value θ of random generation before obtaining Jacobi transposed matrix moduleinit, and enable θ=θinit；
Joint variable θ is brought into robot forward kinematics equation, corresponding pose P is obtainedinit；
Calculate pose PinitWith the pose deviation delta e=P-P of object pose PinitAnd the mould error of pose deviation delta e；
Judge whether mould error meets error < Threshold, if it is, exporting joint variable θ and terminating, otherwise, calls
The acquisition Jacobi transposed matrix module.
8. the rapid solving system of high-freedom degree Robotic inverse kinematics as claimed in claim 6, which is characterized in that described to obtain
It obtains and each speculates value in pose tolerance module greater than 0, less than 1.
9. the rapid solving system of high-freedom degree Robotic inverse kinematics as claimed in claim 6, which is characterized in that described to obtain
Be in pose tolerance module the corresponding joint variable updated value of each congenial value calculating formula are as follows:
Δθk=αkJTΔe
Wherein Δ θkFor joint variable updated value, αkTo speculate value, JTFor Jacobi transposed matrix, Δ e is pose deviation.
10. the rapid solving system of high-freedom degree Robotic inverse kinematics as claimed in claim 6, which is characterized in that open m
A computational threads, per thread generates one and speculates value, wherein k-th of thread generates and speculate value αk, calculation formula are as follows:
Wherein αkTo speculate value, Δ e is pose deviation, JTFor Jacobi transposed matrix, J is Jacobian matrix.
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| CN107351089B (en) * | 2017-09-12 | 2019-08-27 | 中国科学技术大学 | A kind of robot kinematics' parameter calibration pose optimum option method |
| CN109366486B (en) * | 2018-09-28 | 2021-12-07 | 哈尔滨工业大学（深圳） | Flexible robot inverse kinematics solving method, system, equipment and storage medium |
| CN109822571B (en) * | 2019-02-18 | 2020-12-08 | 中国铁建重工集团股份有限公司 | Control method, device and equipment for mechanical arm of assembling machine |
| CN110531866B (en) * | 2019-10-29 | 2020-03-13 | 深圳市瑞立视多媒体科技有限公司 | Method for performing attitude calculation based on improved inverse kinematics and related equipment |
| CN111230860B (en) * | 2020-01-02 | 2022-03-01 | 腾讯科技（深圳）有限公司 | Robot control method, robot control device, computer device, and storage medium |
| CN111890349A (en) * | 2020-05-25 | 2020-11-06 | 北京空间飞行器总体设计部 | Four-degree-of-freedom mechanical arm motion planning method |
| CN113334381B (en) * | 2021-06-01 | 2023-08-01 | 中国科学院沈阳自动化研究所 | Control method of movable decoupling continuum robot |
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